Properties

Label 667.2.a.a.1.7
Level $667$
Weight $2$
Character 667.1
Self dual yes
Analytic conductor $5.326$
Analytic rank $1$
Dimension $10$
CM no
Inner twists $1$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [667,2,Mod(1,667)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(667, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("667.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 667 = 23 \cdot 29 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 667.a (trivial)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: yes
Analytic conductor: \(5.32602181482\)
Analytic rank: \(1\)
Dimension: \(10\)
Coefficient field: \(\mathbb{Q}[x]/(x^{10} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{10} - 3x^{9} - 10x^{8} + 32x^{7} + 32x^{6} - 118x^{5} - 29x^{4} + 182x^{3} - 28x^{2} - 101x + 43 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.7
Root \(-1.31926\) of defining polynomial
Character \(\chi\) \(=\) 667.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+1.31926 q^{2} +1.82466 q^{3} -0.259562 q^{4} -4.11119 q^{5} +2.40720 q^{6} -2.74867 q^{7} -2.98094 q^{8} +0.329400 q^{9} +O(q^{10})\) \(q+1.31926 q^{2} +1.82466 q^{3} -0.259562 q^{4} -4.11119 q^{5} +2.40720 q^{6} -2.74867 q^{7} -2.98094 q^{8} +0.329400 q^{9} -5.42371 q^{10} +4.56858 q^{11} -0.473613 q^{12} -6.36237 q^{13} -3.62620 q^{14} -7.50154 q^{15} -3.41350 q^{16} -3.25232 q^{17} +0.434564 q^{18} +6.59861 q^{19} +1.06711 q^{20} -5.01540 q^{21} +6.02713 q^{22} +1.00000 q^{23} -5.43922 q^{24} +11.9019 q^{25} -8.39360 q^{26} -4.87295 q^{27} +0.713450 q^{28} +1.00000 q^{29} -9.89645 q^{30} -9.08138 q^{31} +1.45860 q^{32} +8.33613 q^{33} -4.29064 q^{34} +11.3003 q^{35} -0.0854998 q^{36} +6.61278 q^{37} +8.70526 q^{38} -11.6092 q^{39} +12.2552 q^{40} -2.61975 q^{41} -6.61660 q^{42} -8.65344 q^{43} -1.18583 q^{44} -1.35423 q^{45} +1.31926 q^{46} -5.78296 q^{47} -6.22850 q^{48} +0.555185 q^{49} +15.7016 q^{50} -5.93439 q^{51} +1.65143 q^{52} +1.33533 q^{53} -6.42867 q^{54} -18.7823 q^{55} +8.19363 q^{56} +12.0403 q^{57} +1.31926 q^{58} +7.66955 q^{59} +1.94711 q^{60} +5.22375 q^{61} -11.9807 q^{62} -0.905413 q^{63} +8.75127 q^{64} +26.1569 q^{65} +10.9975 q^{66} +1.97447 q^{67} +0.844178 q^{68} +1.82466 q^{69} +14.9080 q^{70} -4.65159 q^{71} -0.981924 q^{72} -6.95340 q^{73} +8.72396 q^{74} +21.7169 q^{75} -1.71275 q^{76} -12.5575 q^{77} -15.3155 q^{78} +9.90285 q^{79} +14.0336 q^{80} -9.87970 q^{81} -3.45613 q^{82} -11.5122 q^{83} +1.30181 q^{84} +13.3709 q^{85} -11.4161 q^{86} +1.82466 q^{87} -13.6187 q^{88} -2.94778 q^{89} -1.78657 q^{90} +17.4881 q^{91} -0.259562 q^{92} -16.5705 q^{93} -7.62921 q^{94} -27.1281 q^{95} +2.66145 q^{96} +2.26492 q^{97} +0.732432 q^{98} +1.50489 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 10 q - 3 q^{2} - 9 q^{3} + 9 q^{4} - 10 q^{5} + 4 q^{6} + q^{7} - 9 q^{8} + 7 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 10 q - 3 q^{2} - 9 q^{3} + 9 q^{4} - 10 q^{5} + 4 q^{6} + q^{7} - 9 q^{8} + 7 q^{9} - 6 q^{10} - 17 q^{12} - 13 q^{13} - 12 q^{14} + 2 q^{15} - 5 q^{16} - 22 q^{17} + 12 q^{18} - 2 q^{19} + 3 q^{20} - 7 q^{21} + 3 q^{22} + 10 q^{23} - 6 q^{24} + 10 q^{25} - 25 q^{26} - 24 q^{27} + 19 q^{28} + 10 q^{29} - 3 q^{30} - 22 q^{31} - 31 q^{32} - 9 q^{33} + 13 q^{34} - 15 q^{35} + 19 q^{36} - 9 q^{37} - 10 q^{38} + 4 q^{39} - 6 q^{40} - 25 q^{41} - 34 q^{42} + 3 q^{43} - 27 q^{44} - 28 q^{45} - 3 q^{46} - 17 q^{47} - 3 q^{48} + 17 q^{49} + 2 q^{50} + 38 q^{51} - 18 q^{52} - 43 q^{53} - 47 q^{54} - 11 q^{55} - 7 q^{56} + 18 q^{57} - 3 q^{58} - 7 q^{59} - 21 q^{60} - 6 q^{61} + 3 q^{62} + 11 q^{63} + 33 q^{64} + 11 q^{65} + 55 q^{66} + 11 q^{67} - 51 q^{68} - 9 q^{69} + 34 q^{70} - 17 q^{71} + 34 q^{72} - 44 q^{73} + 9 q^{74} + q^{75} + 24 q^{76} - 71 q^{77} + 38 q^{78} + 5 q^{79} + 38 q^{80} + 18 q^{81} + 33 q^{82} - 32 q^{83} + 14 q^{84} + 16 q^{85} - 9 q^{86} - 9 q^{87} + 18 q^{88} - 10 q^{89} - 9 q^{90} - 3 q^{91} + 9 q^{92} - 8 q^{93} + 47 q^{94} - 8 q^{95} + 60 q^{96} + 6 q^{97} - 73 q^{98} + 26 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.31926 0.932855 0.466428 0.884559i \(-0.345541\pi\)
0.466428 + 0.884559i \(0.345541\pi\)
\(3\) 1.82466 1.05347 0.526735 0.850029i \(-0.323416\pi\)
0.526735 + 0.850029i \(0.323416\pi\)
\(4\) −0.259562 −0.129781
\(5\) −4.11119 −1.83858 −0.919289 0.393582i \(-0.871236\pi\)
−0.919289 + 0.393582i \(0.871236\pi\)
\(6\) 2.40720 0.982736
\(7\) −2.74867 −1.03890 −0.519450 0.854501i \(-0.673863\pi\)
−0.519450 + 0.854501i \(0.673863\pi\)
\(8\) −2.98094 −1.05392
\(9\) 0.329400 0.109800
\(10\) −5.42371 −1.71513
\(11\) 4.56858 1.37748 0.688740 0.725009i \(-0.258164\pi\)
0.688740 + 0.725009i \(0.258164\pi\)
\(12\) −0.473613 −0.136720
\(13\) −6.36237 −1.76460 −0.882302 0.470683i \(-0.844007\pi\)
−0.882302 + 0.470683i \(0.844007\pi\)
\(14\) −3.62620 −0.969143
\(15\) −7.50154 −1.93689
\(16\) −3.41350 −0.853376
\(17\) −3.25232 −0.788803 −0.394402 0.918938i \(-0.629048\pi\)
−0.394402 + 0.918938i \(0.629048\pi\)
\(18\) 0.434564 0.102428
\(19\) 6.59861 1.51383 0.756913 0.653516i \(-0.226707\pi\)
0.756913 + 0.653516i \(0.226707\pi\)
\(20\) 1.06711 0.238613
\(21\) −5.01540 −1.09445
\(22\) 6.02713 1.28499
\(23\) 1.00000 0.208514
\(24\) −5.43922 −1.11028
\(25\) 11.9019 2.38037
\(26\) −8.39360 −1.64612
\(27\) −4.87295 −0.937799
\(28\) 0.713450 0.134829
\(29\) 1.00000 0.185695
\(30\) −9.89645 −1.80684
\(31\) −9.08138 −1.63106 −0.815532 0.578712i \(-0.803556\pi\)
−0.815532 + 0.578712i \(0.803556\pi\)
\(32\) 1.45860 0.257846
\(33\) 8.33613 1.45113
\(34\) −4.29064 −0.735839
\(35\) 11.3003 1.91010
\(36\) −0.0854998 −0.0142500
\(37\) 6.61278 1.08714 0.543568 0.839365i \(-0.317073\pi\)
0.543568 + 0.839365i \(0.317073\pi\)
\(38\) 8.70526 1.41218
\(39\) −11.6092 −1.85896
\(40\) 12.2552 1.93772
\(41\) −2.61975 −0.409137 −0.204568 0.978852i \(-0.565579\pi\)
−0.204568 + 0.978852i \(0.565579\pi\)
\(42\) −6.61660 −1.02096
\(43\) −8.65344 −1.31964 −0.659819 0.751425i \(-0.729367\pi\)
−0.659819 + 0.751425i \(0.729367\pi\)
\(44\) −1.18583 −0.178771
\(45\) −1.35423 −0.201876
\(46\) 1.31926 0.194514
\(47\) −5.78296 −0.843531 −0.421766 0.906705i \(-0.638590\pi\)
−0.421766 + 0.906705i \(0.638590\pi\)
\(48\) −6.22850 −0.899006
\(49\) 0.555185 0.0793122
\(50\) 15.7016 2.22054
\(51\) −5.93439 −0.830981
\(52\) 1.65143 0.229012
\(53\) 1.33533 0.183422 0.0917111 0.995786i \(-0.470766\pi\)
0.0917111 + 0.995786i \(0.470766\pi\)
\(54\) −6.42867 −0.874831
\(55\) −18.7823 −2.53260
\(56\) 8.19363 1.09492
\(57\) 12.0403 1.59477
\(58\) 1.31926 0.173227
\(59\) 7.66955 0.998491 0.499245 0.866461i \(-0.333611\pi\)
0.499245 + 0.866461i \(0.333611\pi\)
\(60\) 1.94711 0.251371
\(61\) 5.22375 0.668833 0.334416 0.942425i \(-0.391461\pi\)
0.334416 + 0.942425i \(0.391461\pi\)
\(62\) −11.9807 −1.52155
\(63\) −0.905413 −0.114071
\(64\) 8.75127 1.09391
\(65\) 26.1569 3.24436
\(66\) 10.9975 1.35370
\(67\) 1.97447 0.241219 0.120610 0.992700i \(-0.461515\pi\)
0.120610 + 0.992700i \(0.461515\pi\)
\(68\) 0.844178 0.102372
\(69\) 1.82466 0.219664
\(70\) 14.9080 1.78185
\(71\) −4.65159 −0.552042 −0.276021 0.961152i \(-0.589016\pi\)
−0.276021 + 0.961152i \(0.589016\pi\)
\(72\) −0.981924 −0.115721
\(73\) −6.95340 −0.813834 −0.406917 0.913465i \(-0.633396\pi\)
−0.406917 + 0.913465i \(0.633396\pi\)
\(74\) 8.72396 1.01414
\(75\) 21.7169 2.50765
\(76\) −1.71275 −0.196466
\(77\) −12.5575 −1.43106
\(78\) −15.3155 −1.73414
\(79\) 9.90285 1.11416 0.557079 0.830460i \(-0.311922\pi\)
0.557079 + 0.830460i \(0.311922\pi\)
\(80\) 14.0336 1.56900
\(81\) −9.87970 −1.09774
\(82\) −3.45613 −0.381665
\(83\) −11.5122 −1.26363 −0.631816 0.775119i \(-0.717690\pi\)
−0.631816 + 0.775119i \(0.717690\pi\)
\(84\) 1.30181 0.142039
\(85\) 13.3709 1.45028
\(86\) −11.4161 −1.23103
\(87\) 1.82466 0.195625
\(88\) −13.6187 −1.45176
\(89\) −2.94778 −0.312464 −0.156232 0.987720i \(-0.549935\pi\)
−0.156232 + 0.987720i \(0.549935\pi\)
\(90\) −1.78657 −0.188321
\(91\) 17.4881 1.83325
\(92\) −0.259562 −0.0270612
\(93\) −16.5705 −1.71828
\(94\) −7.62921 −0.786893
\(95\) −27.1281 −2.78329
\(96\) 2.66145 0.271633
\(97\) 2.26492 0.229968 0.114984 0.993367i \(-0.463318\pi\)
0.114984 + 0.993367i \(0.463318\pi\)
\(98\) 0.732432 0.0739868
\(99\) 1.50489 0.151247
\(100\) −3.08927 −0.308927
\(101\) −0.171130 −0.0170281 −0.00851403 0.999964i \(-0.502710\pi\)
−0.00851403 + 0.999964i \(0.502710\pi\)
\(102\) −7.82898 −0.775185
\(103\) −14.1919 −1.39837 −0.699187 0.714939i \(-0.746454\pi\)
−0.699187 + 0.714939i \(0.746454\pi\)
\(104\) 18.9659 1.85976
\(105\) 20.6193 2.01223
\(106\) 1.76165 0.171106
\(107\) −4.01155 −0.387811 −0.193906 0.981020i \(-0.562116\pi\)
−0.193906 + 0.981020i \(0.562116\pi\)
\(108\) 1.26483 0.121708
\(109\) −1.73215 −0.165910 −0.0829551 0.996553i \(-0.526436\pi\)
−0.0829551 + 0.996553i \(0.526436\pi\)
\(110\) −24.7787 −2.36255
\(111\) 12.0661 1.14526
\(112\) 9.38259 0.886572
\(113\) −3.63931 −0.342358 −0.171179 0.985240i \(-0.554758\pi\)
−0.171179 + 0.985240i \(0.554758\pi\)
\(114\) 15.8842 1.48769
\(115\) −4.11119 −0.383370
\(116\) −0.259562 −0.0240997
\(117\) −2.09577 −0.193754
\(118\) 10.1181 0.931447
\(119\) 8.93955 0.819487
\(120\) 22.3616 2.04133
\(121\) 9.87194 0.897449
\(122\) 6.89147 0.623924
\(123\) −4.78017 −0.431013
\(124\) 2.35718 0.211681
\(125\) −28.3749 −2.53792
\(126\) −1.19447 −0.106412
\(127\) 2.40280 0.213214 0.106607 0.994301i \(-0.466001\pi\)
0.106607 + 0.994301i \(0.466001\pi\)
\(128\) 8.62798 0.762613
\(129\) −15.7896 −1.39020
\(130\) 34.5077 3.02652
\(131\) −15.6553 −1.36781 −0.683907 0.729569i \(-0.739721\pi\)
−0.683907 + 0.729569i \(0.739721\pi\)
\(132\) −2.16374 −0.188330
\(133\) −18.1374 −1.57271
\(134\) 2.60483 0.225023
\(135\) 20.0336 1.72422
\(136\) 9.69497 0.831337
\(137\) −20.2050 −1.72623 −0.863113 0.505010i \(-0.831489\pi\)
−0.863113 + 0.505010i \(0.831489\pi\)
\(138\) 2.40720 0.204915
\(139\) 8.94680 0.758857 0.379429 0.925221i \(-0.376121\pi\)
0.379429 + 0.925221i \(0.376121\pi\)
\(140\) −2.93313 −0.247894
\(141\) −10.5520 −0.888635
\(142\) −6.13664 −0.514976
\(143\) −29.0670 −2.43071
\(144\) −1.12441 −0.0937008
\(145\) −4.11119 −0.341416
\(146\) −9.17332 −0.759189
\(147\) 1.01303 0.0835531
\(148\) −1.71643 −0.141089
\(149\) 8.40338 0.688432 0.344216 0.938890i \(-0.388145\pi\)
0.344216 + 0.938890i \(0.388145\pi\)
\(150\) 28.6502 2.33928
\(151\) 0.901268 0.0733442 0.0366721 0.999327i \(-0.488324\pi\)
0.0366721 + 0.999327i \(0.488324\pi\)
\(152\) −19.6701 −1.59545
\(153\) −1.07132 −0.0866107
\(154\) −16.5666 −1.33497
\(155\) 37.3353 2.99884
\(156\) 3.01330 0.241257
\(157\) 22.4829 1.79433 0.897164 0.441697i \(-0.145623\pi\)
0.897164 + 0.441697i \(0.145623\pi\)
\(158\) 13.0644 1.03935
\(159\) 2.43654 0.193230
\(160\) −5.99656 −0.474070
\(161\) −2.74867 −0.216626
\(162\) −13.0339 −1.02404
\(163\) −7.39140 −0.578939 −0.289470 0.957187i \(-0.593479\pi\)
−0.289470 + 0.957187i \(0.593479\pi\)
\(164\) 0.679988 0.0530981
\(165\) −34.2714 −2.66802
\(166\) −15.1876 −1.17878
\(167\) −1.89972 −0.147004 −0.0735022 0.997295i \(-0.523418\pi\)
−0.0735022 + 0.997295i \(0.523418\pi\)
\(168\) 14.9506 1.15347
\(169\) 27.4798 2.11383
\(170\) 17.6396 1.35290
\(171\) 2.17359 0.166218
\(172\) 2.24610 0.171264
\(173\) −0.795280 −0.0604641 −0.0302320 0.999543i \(-0.509625\pi\)
−0.0302320 + 0.999543i \(0.509625\pi\)
\(174\) 2.40720 0.182489
\(175\) −32.7143 −2.47297
\(176\) −15.5949 −1.17551
\(177\) 13.9944 1.05188
\(178\) −3.88888 −0.291484
\(179\) −6.16453 −0.460759 −0.230379 0.973101i \(-0.573997\pi\)
−0.230379 + 0.973101i \(0.573997\pi\)
\(180\) 0.351506 0.0261997
\(181\) −17.0943 −1.27061 −0.635304 0.772262i \(-0.719125\pi\)
−0.635304 + 0.772262i \(0.719125\pi\)
\(182\) 23.0712 1.71015
\(183\) 9.53159 0.704596
\(184\) −2.98094 −0.219758
\(185\) −27.1864 −1.99878
\(186\) −21.8607 −1.60291
\(187\) −14.8585 −1.08656
\(188\) 1.50104 0.109474
\(189\) 13.3941 0.974279
\(190\) −35.7890 −2.59640
\(191\) 4.58496 0.331756 0.165878 0.986146i \(-0.446954\pi\)
0.165878 + 0.986146i \(0.446954\pi\)
\(192\) 15.9681 1.15240
\(193\) 14.8598 1.06963 0.534817 0.844968i \(-0.320381\pi\)
0.534817 + 0.844968i \(0.320381\pi\)
\(194\) 2.98801 0.214527
\(195\) 47.7276 3.41784
\(196\) −0.144105 −0.0102932
\(197\) −16.8176 −1.19820 −0.599101 0.800674i \(-0.704475\pi\)
−0.599101 + 0.800674i \(0.704475\pi\)
\(198\) 1.98534 0.141092
\(199\) 10.6701 0.756386 0.378193 0.925727i \(-0.376546\pi\)
0.378193 + 0.925727i \(0.376546\pi\)
\(200\) −35.4788 −2.50873
\(201\) 3.60274 0.254118
\(202\) −0.225764 −0.0158847
\(203\) −2.74867 −0.192919
\(204\) 1.54034 0.107845
\(205\) 10.7703 0.752230
\(206\) −18.7228 −1.30448
\(207\) 0.329400 0.0228949
\(208\) 21.7180 1.50587
\(209\) 30.1463 2.08526
\(210\) 27.2021 1.87712
\(211\) −24.1044 −1.65942 −0.829709 0.558197i \(-0.811493\pi\)
−0.829709 + 0.558197i \(0.811493\pi\)
\(212\) −0.346602 −0.0238047
\(213\) −8.48760 −0.581560
\(214\) −5.29226 −0.361772
\(215\) 35.5759 2.42626
\(216\) 14.5260 0.988367
\(217\) 24.9617 1.69451
\(218\) −2.28516 −0.154770
\(219\) −12.6876 −0.857350
\(220\) 4.87517 0.328684
\(221\) 20.6925 1.39193
\(222\) 15.9183 1.06837
\(223\) 0.944548 0.0632516 0.0316258 0.999500i \(-0.489932\pi\)
0.0316258 + 0.999500i \(0.489932\pi\)
\(224\) −4.00920 −0.267876
\(225\) 3.92048 0.261365
\(226\) −4.80119 −0.319370
\(227\) 20.3135 1.34825 0.674126 0.738617i \(-0.264521\pi\)
0.674126 + 0.738617i \(0.264521\pi\)
\(228\) −3.12519 −0.206971
\(229\) 6.86545 0.453682 0.226841 0.973932i \(-0.427160\pi\)
0.226841 + 0.973932i \(0.427160\pi\)
\(230\) −5.42371 −0.357629
\(231\) −22.9133 −1.50758
\(232\) −2.98094 −0.195708
\(233\) −9.87907 −0.647199 −0.323600 0.946194i \(-0.604893\pi\)
−0.323600 + 0.946194i \(0.604893\pi\)
\(234\) −2.76486 −0.180744
\(235\) 23.7748 1.55090
\(236\) −1.99072 −0.129585
\(237\) 18.0694 1.17373
\(238\) 11.7936 0.764463
\(239\) 9.96016 0.644269 0.322134 0.946694i \(-0.395600\pi\)
0.322134 + 0.946694i \(0.395600\pi\)
\(240\) 25.6065 1.65289
\(241\) 6.96142 0.448425 0.224212 0.974540i \(-0.428019\pi\)
0.224212 + 0.974540i \(0.428019\pi\)
\(242\) 13.0236 0.837190
\(243\) −3.40829 −0.218642
\(244\) −1.35589 −0.0868018
\(245\) −2.28247 −0.145822
\(246\) −6.30627 −0.402073
\(247\) −41.9828 −2.67130
\(248\) 27.0711 1.71901
\(249\) −21.0060 −1.33120
\(250\) −37.4337 −2.36752
\(251\) 10.0183 0.632352 0.316176 0.948701i \(-0.397601\pi\)
0.316176 + 0.948701i \(0.397601\pi\)
\(252\) 0.235011 0.0148043
\(253\) 4.56858 0.287224
\(254\) 3.16991 0.198898
\(255\) 24.3974 1.52782
\(256\) −6.12002 −0.382501
\(257\) −4.87303 −0.303971 −0.151986 0.988383i \(-0.548567\pi\)
−0.151986 + 0.988383i \(0.548567\pi\)
\(258\) −20.8306 −1.29685
\(259\) −18.1764 −1.12942
\(260\) −6.78934 −0.421057
\(261\) 0.329400 0.0203894
\(262\) −20.6534 −1.27597
\(263\) 5.63631 0.347549 0.173775 0.984785i \(-0.444404\pi\)
0.173775 + 0.984785i \(0.444404\pi\)
\(264\) −24.8495 −1.52938
\(265\) −5.48981 −0.337236
\(266\) −23.9279 −1.46711
\(267\) −5.37872 −0.329172
\(268\) −0.512496 −0.0313057
\(269\) −20.0520 −1.22259 −0.611296 0.791402i \(-0.709352\pi\)
−0.611296 + 0.791402i \(0.709352\pi\)
\(270\) 26.4295 1.60845
\(271\) 12.8081 0.778039 0.389020 0.921229i \(-0.372814\pi\)
0.389020 + 0.921229i \(0.372814\pi\)
\(272\) 11.1018 0.673146
\(273\) 31.9098 1.93127
\(274\) −26.6555 −1.61032
\(275\) 54.3746 3.27891
\(276\) −0.473613 −0.0285082
\(277\) 13.1150 0.788002 0.394001 0.919110i \(-0.371091\pi\)
0.394001 + 0.919110i \(0.371091\pi\)
\(278\) 11.8031 0.707904
\(279\) −2.99141 −0.179091
\(280\) −33.6855 −2.01310
\(281\) 3.97492 0.237124 0.118562 0.992947i \(-0.462172\pi\)
0.118562 + 0.992947i \(0.462172\pi\)
\(282\) −13.9207 −0.828968
\(283\) −4.04216 −0.240281 −0.120141 0.992757i \(-0.538335\pi\)
−0.120141 + 0.992757i \(0.538335\pi\)
\(284\) 1.20738 0.0716446
\(285\) −49.4997 −2.93211
\(286\) −38.3469 −2.26750
\(287\) 7.20083 0.425052
\(288\) 0.480462 0.0283115
\(289\) −6.42243 −0.377790
\(290\) −5.42371 −0.318491
\(291\) 4.13272 0.242264
\(292\) 1.80484 0.105620
\(293\) 8.95096 0.522921 0.261460 0.965214i \(-0.415796\pi\)
0.261460 + 0.965214i \(0.415796\pi\)
\(294\) 1.33644 0.0779429
\(295\) −31.5310 −1.83580
\(296\) −19.7123 −1.14576
\(297\) −22.2625 −1.29180
\(298\) 11.0862 0.642207
\(299\) −6.36237 −0.367945
\(300\) −5.63688 −0.325445
\(301\) 23.7855 1.37097
\(302\) 1.18900 0.0684195
\(303\) −0.312255 −0.0179386
\(304\) −22.5244 −1.29186
\(305\) −21.4758 −1.22970
\(306\) −1.41334 −0.0807952
\(307\) 3.10039 0.176949 0.0884743 0.996078i \(-0.471801\pi\)
0.0884743 + 0.996078i \(0.471801\pi\)
\(308\) 3.25945 0.185725
\(309\) −25.8955 −1.47314
\(310\) 49.2548 2.79748
\(311\) −4.41722 −0.250478 −0.125239 0.992127i \(-0.539970\pi\)
−0.125239 + 0.992127i \(0.539970\pi\)
\(312\) 34.6063 1.95920
\(313\) 12.0162 0.679194 0.339597 0.940571i \(-0.389709\pi\)
0.339597 + 0.940571i \(0.389709\pi\)
\(314\) 29.6607 1.67385
\(315\) 3.72232 0.209729
\(316\) −2.57040 −0.144596
\(317\) 28.1477 1.58093 0.790466 0.612506i \(-0.209839\pi\)
0.790466 + 0.612506i \(0.209839\pi\)
\(318\) 3.21442 0.180256
\(319\) 4.56858 0.255791
\(320\) −35.9781 −2.01124
\(321\) −7.31973 −0.408548
\(322\) −3.62620 −0.202080
\(323\) −21.4608 −1.19411
\(324\) 2.56439 0.142466
\(325\) −75.7241 −4.20042
\(326\) −9.75115 −0.540066
\(327\) −3.16060 −0.174782
\(328\) 7.80933 0.431198
\(329\) 15.8954 0.876344
\(330\) −45.2128 −2.48888
\(331\) 18.5216 1.01804 0.509019 0.860755i \(-0.330008\pi\)
0.509019 + 0.860755i \(0.330008\pi\)
\(332\) 2.98814 0.163995
\(333\) 2.17825 0.119368
\(334\) −2.50621 −0.137134
\(335\) −8.11740 −0.443501
\(336\) 17.1201 0.933977
\(337\) −5.49971 −0.299588 −0.149794 0.988717i \(-0.547861\pi\)
−0.149794 + 0.988717i \(0.547861\pi\)
\(338\) 36.2529 1.97190
\(339\) −6.64052 −0.360664
\(340\) −3.47057 −0.188218
\(341\) −41.4890 −2.24676
\(342\) 2.86752 0.155058
\(343\) 17.7147 0.956502
\(344\) 25.7954 1.39080
\(345\) −7.50154 −0.403869
\(346\) −1.04918 −0.0564042
\(347\) −21.8641 −1.17373 −0.586863 0.809686i \(-0.699637\pi\)
−0.586863 + 0.809686i \(0.699637\pi\)
\(348\) −0.473613 −0.0253883
\(349\) 20.1439 1.07828 0.539138 0.842217i \(-0.318750\pi\)
0.539138 + 0.842217i \(0.318750\pi\)
\(350\) −43.1585 −2.30692
\(351\) 31.0035 1.65484
\(352\) 6.66372 0.355177
\(353\) −11.2359 −0.598029 −0.299014 0.954249i \(-0.596658\pi\)
−0.299014 + 0.954249i \(0.596658\pi\)
\(354\) 18.4622 0.981252
\(355\) 19.1236 1.01497
\(356\) 0.765132 0.0405519
\(357\) 16.3117 0.863305
\(358\) −8.13260 −0.429821
\(359\) −30.9360 −1.63274 −0.816369 0.577531i \(-0.804016\pi\)
−0.816369 + 0.577531i \(0.804016\pi\)
\(360\) 4.03687 0.212762
\(361\) 24.5417 1.29167
\(362\) −22.5517 −1.18529
\(363\) 18.0130 0.945436
\(364\) −4.53923 −0.237921
\(365\) 28.5867 1.49630
\(366\) 12.5746 0.657286
\(367\) −22.8506 −1.19279 −0.596396 0.802691i \(-0.703401\pi\)
−0.596396 + 0.802691i \(0.703401\pi\)
\(368\) −3.41350 −0.177941
\(369\) −0.862947 −0.0449233
\(370\) −35.8658 −1.86458
\(371\) −3.67039 −0.190557
\(372\) 4.30106 0.223000
\(373\) −7.59121 −0.393058 −0.196529 0.980498i \(-0.562967\pi\)
−0.196529 + 0.980498i \(0.562967\pi\)
\(374\) −19.6021 −1.01360
\(375\) −51.7746 −2.67363
\(376\) 17.2387 0.889016
\(377\) −6.36237 −0.327679
\(378\) 17.6703 0.908862
\(379\) −14.5273 −0.746216 −0.373108 0.927788i \(-0.621708\pi\)
−0.373108 + 0.927788i \(0.621708\pi\)
\(380\) 7.04143 0.361218
\(381\) 4.38431 0.224615
\(382\) 6.04874 0.309481
\(383\) −32.5891 −1.66523 −0.832614 0.553854i \(-0.813157\pi\)
−0.832614 + 0.553854i \(0.813157\pi\)
\(384\) 15.7432 0.803390
\(385\) 51.6263 2.63112
\(386\) 19.6039 0.997814
\(387\) −2.85045 −0.144896
\(388\) −0.587887 −0.0298454
\(389\) −29.9827 −1.52018 −0.760092 0.649816i \(-0.774846\pi\)
−0.760092 + 0.649816i \(0.774846\pi\)
\(390\) 62.9649 3.18835
\(391\) −3.25232 −0.164477
\(392\) −1.65498 −0.0835889
\(393\) −28.5658 −1.44095
\(394\) −22.1867 −1.11775
\(395\) −40.7125 −2.04847
\(396\) −0.390613 −0.0196290
\(397\) 2.70605 0.135813 0.0679063 0.997692i \(-0.478368\pi\)
0.0679063 + 0.997692i \(0.478368\pi\)
\(398\) 14.0767 0.705599
\(399\) −33.0947 −1.65681
\(400\) −40.6271 −2.03135
\(401\) 20.8363 1.04052 0.520259 0.854009i \(-0.325836\pi\)
0.520259 + 0.854009i \(0.325836\pi\)
\(402\) 4.75294 0.237055
\(403\) 57.7791 2.87818
\(404\) 0.0444188 0.00220992
\(405\) 40.6173 2.01829
\(406\) −3.62620 −0.179965
\(407\) 30.2110 1.49751
\(408\) 17.6901 0.875789
\(409\) −8.56957 −0.423738 −0.211869 0.977298i \(-0.567955\pi\)
−0.211869 + 0.977298i \(0.567955\pi\)
\(410\) 14.2088 0.701722
\(411\) −36.8673 −1.81853
\(412\) 3.68369 0.181482
\(413\) −21.0811 −1.03733
\(414\) 0.434564 0.0213576
\(415\) 47.3289 2.32329
\(416\) −9.28013 −0.454996
\(417\) 16.3249 0.799434
\(418\) 39.7707 1.94525
\(419\) 13.0013 0.635157 0.317578 0.948232i \(-0.397130\pi\)
0.317578 + 0.948232i \(0.397130\pi\)
\(420\) −5.35197 −0.261149
\(421\) 22.6385 1.10333 0.551667 0.834064i \(-0.313992\pi\)
0.551667 + 0.834064i \(0.313992\pi\)
\(422\) −31.7999 −1.54800
\(423\) −1.90491 −0.0926199
\(424\) −3.98055 −0.193313
\(425\) −38.7086 −1.87764
\(426\) −11.1973 −0.542512
\(427\) −14.3584 −0.694850
\(428\) 1.04125 0.0503305
\(429\) −53.0376 −2.56068
\(430\) 46.9338 2.26335
\(431\) −31.8549 −1.53439 −0.767197 0.641411i \(-0.778349\pi\)
−0.767197 + 0.641411i \(0.778349\pi\)
\(432\) 16.6338 0.800295
\(433\) −14.0708 −0.676200 −0.338100 0.941110i \(-0.609784\pi\)
−0.338100 + 0.941110i \(0.609784\pi\)
\(434\) 32.9309 1.58073
\(435\) −7.50154 −0.359671
\(436\) 0.449601 0.0215320
\(437\) 6.59861 0.315654
\(438\) −16.7382 −0.799783
\(439\) 8.82152 0.421028 0.210514 0.977591i \(-0.432486\pi\)
0.210514 + 0.977591i \(0.432486\pi\)
\(440\) 55.9889 2.66917
\(441\) 0.182878 0.00870849
\(442\) 27.2987 1.29847
\(443\) −33.8771 −1.60955 −0.804776 0.593579i \(-0.797715\pi\)
−0.804776 + 0.593579i \(0.797715\pi\)
\(444\) −3.13190 −0.148634
\(445\) 12.1189 0.574491
\(446\) 1.24610 0.0590046
\(447\) 15.3334 0.725243
\(448\) −24.0544 −1.13646
\(449\) 3.91466 0.184744 0.0923721 0.995725i \(-0.470555\pi\)
0.0923721 + 0.995725i \(0.470555\pi\)
\(450\) 5.17212 0.243816
\(451\) −11.9686 −0.563577
\(452\) 0.944627 0.0444315
\(453\) 1.64451 0.0772659
\(454\) 26.7987 1.25772
\(455\) −71.8967 −3.37057
\(456\) −35.8913 −1.68076
\(457\) −19.8594 −0.928985 −0.464493 0.885577i \(-0.653763\pi\)
−0.464493 + 0.885577i \(0.653763\pi\)
\(458\) 9.05729 0.423219
\(459\) 15.8484 0.739739
\(460\) 1.06711 0.0497542
\(461\) −16.4586 −0.766553 −0.383277 0.923634i \(-0.625204\pi\)
−0.383277 + 0.923634i \(0.625204\pi\)
\(462\) −30.2285 −1.40636
\(463\) 25.4972 1.18496 0.592478 0.805587i \(-0.298150\pi\)
0.592478 + 0.805587i \(0.298150\pi\)
\(464\) −3.41350 −0.158468
\(465\) 68.1243 3.15919
\(466\) −13.0330 −0.603743
\(467\) −22.8174 −1.05586 −0.527931 0.849287i \(-0.677032\pi\)
−0.527931 + 0.849287i \(0.677032\pi\)
\(468\) 0.543982 0.0251456
\(469\) −5.42715 −0.250603
\(470\) 31.3651 1.44676
\(471\) 41.0237 1.89027
\(472\) −22.8625 −1.05233
\(473\) −39.5340 −1.81777
\(474\) 23.8381 1.09492
\(475\) 78.5358 3.60347
\(476\) −2.32037 −0.106354
\(477\) 0.439860 0.0201398
\(478\) 13.1400 0.601010
\(479\) 43.4778 1.98655 0.993276 0.115770i \(-0.0369335\pi\)
0.993276 + 0.115770i \(0.0369335\pi\)
\(480\) −10.9417 −0.499419
\(481\) −42.0730 −1.91836
\(482\) 9.18390 0.418315
\(483\) −5.01540 −0.228209
\(484\) −2.56238 −0.116472
\(485\) −9.31151 −0.422814
\(486\) −4.49641 −0.203961
\(487\) −1.07464 −0.0486965 −0.0243482 0.999704i \(-0.507751\pi\)
−0.0243482 + 0.999704i \(0.507751\pi\)
\(488\) −15.5717 −0.704898
\(489\) −13.4868 −0.609895
\(490\) −3.01117 −0.136031
\(491\) 12.4335 0.561117 0.280558 0.959837i \(-0.409480\pi\)
0.280558 + 0.959837i \(0.409480\pi\)
\(492\) 1.24075 0.0559373
\(493\) −3.25232 −0.146477
\(494\) −55.3861 −2.49194
\(495\) −6.18690 −0.278080
\(496\) 30.9993 1.39191
\(497\) 12.7857 0.573517
\(498\) −27.7122 −1.24182
\(499\) −7.45558 −0.333758 −0.166879 0.985977i \(-0.553369\pi\)
−0.166879 + 0.985977i \(0.553369\pi\)
\(500\) 7.36503 0.329374
\(501\) −3.46634 −0.154865
\(502\) 13.2168 0.589893
\(503\) 39.4744 1.76008 0.880039 0.474901i \(-0.157516\pi\)
0.880039 + 0.474901i \(0.157516\pi\)
\(504\) 2.69898 0.120222
\(505\) 0.703547 0.0313074
\(506\) 6.02713 0.267939
\(507\) 50.1414 2.22686
\(508\) −0.623676 −0.0276711
\(509\) −43.4583 −1.92625 −0.963127 0.269047i \(-0.913291\pi\)
−0.963127 + 0.269047i \(0.913291\pi\)
\(510\) 32.1864 1.42524
\(511\) 19.1126 0.845491
\(512\) −25.3298 −1.11943
\(513\) −32.1547 −1.41966
\(514\) −6.42878 −0.283561
\(515\) 58.3457 2.57102
\(516\) 4.09839 0.180421
\(517\) −26.4199 −1.16195
\(518\) −23.9793 −1.05359
\(519\) −1.45112 −0.0636971
\(520\) −77.9722 −3.41931
\(521\) −34.6729 −1.51905 −0.759525 0.650478i \(-0.774568\pi\)
−0.759525 + 0.650478i \(0.774568\pi\)
\(522\) 0.434564 0.0190203
\(523\) 0.0232653 0.00101732 0.000508660 1.00000i \(-0.499838\pi\)
0.000508660 1.00000i \(0.499838\pi\)
\(524\) 4.06353 0.177516
\(525\) −59.6926 −2.60520
\(526\) 7.43573 0.324213
\(527\) 29.5355 1.28659
\(528\) −28.4554 −1.23836
\(529\) 1.00000 0.0434783
\(530\) −7.24247 −0.314593
\(531\) 2.52635 0.109634
\(532\) 4.70778 0.204108
\(533\) 16.6678 0.721964
\(534\) −7.09591 −0.307070
\(535\) 16.4922 0.713022
\(536\) −5.88577 −0.254226
\(537\) −11.2482 −0.485396
\(538\) −26.4537 −1.14050
\(539\) 2.53641 0.109251
\(540\) −5.19996 −0.223771
\(541\) 34.9131 1.50103 0.750515 0.660853i \(-0.229806\pi\)
0.750515 + 0.660853i \(0.229806\pi\)
\(542\) 16.8972 0.725798
\(543\) −31.1913 −1.33855
\(544\) −4.74382 −0.203390
\(545\) 7.12121 0.305039
\(546\) 42.0973 1.80160
\(547\) −10.1866 −0.435547 −0.217774 0.975999i \(-0.569879\pi\)
−0.217774 + 0.975999i \(0.569879\pi\)
\(548\) 5.24444 0.224031
\(549\) 1.72071 0.0734379
\(550\) 71.7341 3.05875
\(551\) 6.59861 0.281110
\(552\) −5.43922 −0.231509
\(553\) −27.2197 −1.15750
\(554\) 17.3020 0.735092
\(555\) −49.6061 −2.10566
\(556\) −2.32225 −0.0984852
\(557\) 11.2100 0.474985 0.237492 0.971389i \(-0.423674\pi\)
0.237492 + 0.971389i \(0.423674\pi\)
\(558\) −3.94644 −0.167066
\(559\) 55.0564 2.32864
\(560\) −38.5736 −1.63003
\(561\) −27.1117 −1.14466
\(562\) 5.24394 0.221202
\(563\) −8.18989 −0.345163 −0.172581 0.984995i \(-0.555211\pi\)
−0.172581 + 0.984995i \(0.555211\pi\)
\(564\) 2.73889 0.115328
\(565\) 14.9619 0.629451
\(566\) −5.33264 −0.224148
\(567\) 27.1560 1.14045
\(568\) 13.8661 0.581810
\(569\) 40.6958 1.70606 0.853028 0.521865i \(-0.174763\pi\)
0.853028 + 0.521865i \(0.174763\pi\)
\(570\) −65.3029 −2.73524
\(571\) −39.4479 −1.65084 −0.825422 0.564516i \(-0.809063\pi\)
−0.825422 + 0.564516i \(0.809063\pi\)
\(572\) 7.54469 0.315459
\(573\) 8.36602 0.349495
\(574\) 9.49975 0.396512
\(575\) 11.9019 0.496342
\(576\) 2.88267 0.120111
\(577\) 36.5420 1.52126 0.760632 0.649183i \(-0.224889\pi\)
0.760632 + 0.649183i \(0.224889\pi\)
\(578\) −8.47283 −0.352423
\(579\) 27.1142 1.12683
\(580\) 1.06711 0.0443092
\(581\) 31.6433 1.31279
\(582\) 5.45212 0.225998
\(583\) 6.10058 0.252660
\(584\) 20.7277 0.857717
\(585\) 8.61610 0.356232
\(586\) 11.8086 0.487810
\(587\) 6.69668 0.276402 0.138201 0.990404i \(-0.455868\pi\)
0.138201 + 0.990404i \(0.455868\pi\)
\(588\) −0.262943 −0.0108436
\(589\) −59.9245 −2.46915
\(590\) −41.5974 −1.71254
\(591\) −30.6864 −1.26227
\(592\) −22.5728 −0.927735
\(593\) 39.0591 1.60397 0.801983 0.597347i \(-0.203778\pi\)
0.801983 + 0.597347i \(0.203778\pi\)
\(594\) −29.3699 −1.20506
\(595\) −36.7522 −1.50669
\(596\) −2.18120 −0.0893454
\(597\) 19.4694 0.796831
\(598\) −8.39360 −0.343240
\(599\) −3.20208 −0.130834 −0.0654168 0.997858i \(-0.520838\pi\)
−0.0654168 + 0.997858i \(0.520838\pi\)
\(600\) −64.7368 −2.64287
\(601\) −27.6424 −1.12756 −0.563778 0.825927i \(-0.690653\pi\)
−0.563778 + 0.825927i \(0.690653\pi\)
\(602\) 31.3791 1.27892
\(603\) 0.650390 0.0264859
\(604\) −0.233935 −0.00951868
\(605\) −40.5854 −1.65003
\(606\) −0.411944 −0.0167341
\(607\) 33.4334 1.35702 0.678510 0.734591i \(-0.262626\pi\)
0.678510 + 0.734591i \(0.262626\pi\)
\(608\) 9.62471 0.390334
\(609\) −5.01540 −0.203234
\(610\) −28.3321 −1.14713
\(611\) 36.7933 1.48850
\(612\) 0.278073 0.0112404
\(613\) −14.7380 −0.595263 −0.297631 0.954681i \(-0.596197\pi\)
−0.297631 + 0.954681i \(0.596197\pi\)
\(614\) 4.09021 0.165067
\(615\) 19.6522 0.792452
\(616\) 37.4332 1.50823
\(617\) −21.9315 −0.882927 −0.441464 0.897279i \(-0.645541\pi\)
−0.441464 + 0.897279i \(0.645541\pi\)
\(618\) −34.1628 −1.37423
\(619\) 31.7740 1.27710 0.638552 0.769578i \(-0.279534\pi\)
0.638552 + 0.769578i \(0.279534\pi\)
\(620\) −9.69081 −0.389192
\(621\) −4.87295 −0.195545
\(622\) −5.82745 −0.233660
\(623\) 8.10248 0.324619
\(624\) 39.6280 1.58639
\(625\) 57.1450 2.28580
\(626\) 15.8524 0.633590
\(627\) 55.0069 2.19676
\(628\) −5.83570 −0.232870
\(629\) −21.5069 −0.857535
\(630\) 4.91070 0.195647
\(631\) −17.8173 −0.709297 −0.354649 0.935000i \(-0.615400\pi\)
−0.354649 + 0.935000i \(0.615400\pi\)
\(632\) −29.5198 −1.17424
\(633\) −43.9825 −1.74815
\(634\) 37.1340 1.47478
\(635\) −9.87836 −0.392011
\(636\) −0.632432 −0.0250776
\(637\) −3.53230 −0.139955
\(638\) 6.02713 0.238616
\(639\) −1.53224 −0.0606143
\(640\) −35.4712 −1.40212
\(641\) −18.3619 −0.725253 −0.362627 0.931935i \(-0.618120\pi\)
−0.362627 + 0.931935i \(0.618120\pi\)
\(642\) −9.65661 −0.381116
\(643\) 33.5879 1.32458 0.662289 0.749248i \(-0.269585\pi\)
0.662289 + 0.749248i \(0.269585\pi\)
\(644\) 0.713450 0.0281139
\(645\) 64.9141 2.55599
\(646\) −28.3123 −1.11393
\(647\) −32.8327 −1.29079 −0.645394 0.763850i \(-0.723307\pi\)
−0.645394 + 0.763850i \(0.723307\pi\)
\(648\) 29.4508 1.15694
\(649\) 35.0390 1.37540
\(650\) −99.8995 −3.91838
\(651\) 45.5468 1.78512
\(652\) 1.91853 0.0751353
\(653\) −11.6542 −0.456064 −0.228032 0.973654i \(-0.573229\pi\)
−0.228032 + 0.973654i \(0.573229\pi\)
\(654\) −4.16964 −0.163046
\(655\) 64.3621 2.51483
\(656\) 8.94253 0.349147
\(657\) −2.29045 −0.0893591
\(658\) 20.9702 0.817502
\(659\) 15.2217 0.592952 0.296476 0.955040i \(-0.404189\pi\)
0.296476 + 0.955040i \(0.404189\pi\)
\(660\) 8.89555 0.346259
\(661\) 13.6959 0.532708 0.266354 0.963875i \(-0.414181\pi\)
0.266354 + 0.963875i \(0.414181\pi\)
\(662\) 24.4347 0.949682
\(663\) 37.7568 1.46635
\(664\) 34.3173 1.33177
\(665\) 74.5663 2.89156
\(666\) 2.87368 0.111353
\(667\) 1.00000 0.0387202
\(668\) 0.493094 0.0190784
\(669\) 1.72348 0.0666337
\(670\) −10.7089 −0.413722
\(671\) 23.8651 0.921303
\(672\) −7.31545 −0.282199
\(673\) 3.63456 0.140102 0.0700510 0.997543i \(-0.477684\pi\)
0.0700510 + 0.997543i \(0.477684\pi\)
\(674\) −7.25553 −0.279472
\(675\) −57.9972 −2.23231
\(676\) −7.13270 −0.274335
\(677\) −25.3809 −0.975467 −0.487734 0.872993i \(-0.662176\pi\)
−0.487734 + 0.872993i \(0.662176\pi\)
\(678\) −8.76055 −0.336447
\(679\) −6.22552 −0.238913
\(680\) −39.8578 −1.52848
\(681\) 37.0652 1.42034
\(682\) −54.7347 −2.09590
\(683\) −3.84356 −0.147070 −0.0735349 0.997293i \(-0.523428\pi\)
−0.0735349 + 0.997293i \(0.523428\pi\)
\(684\) −0.564180 −0.0215720
\(685\) 83.0664 3.17380
\(686\) 23.3702 0.892278
\(687\) 12.5271 0.477940
\(688\) 29.5386 1.12615
\(689\) −8.49589 −0.323668
\(690\) −9.89645 −0.376752
\(691\) −40.4972 −1.54058 −0.770292 0.637691i \(-0.779890\pi\)
−0.770292 + 0.637691i \(0.779890\pi\)
\(692\) 0.206424 0.00784708
\(693\) −4.13645 −0.157131
\(694\) −28.8444 −1.09492
\(695\) −36.7820 −1.39522
\(696\) −5.43922 −0.206173
\(697\) 8.52027 0.322728
\(698\) 26.5749 1.00588
\(699\) −18.0260 −0.681805
\(700\) 8.49138 0.320944
\(701\) −16.8344 −0.635827 −0.317913 0.948120i \(-0.602982\pi\)
−0.317913 + 0.948120i \(0.602982\pi\)
\(702\) 40.9016 1.54373
\(703\) 43.6352 1.64573
\(704\) 39.9809 1.50684
\(705\) 43.3811 1.63383
\(706\) −14.8231 −0.557874
\(707\) 0.470380 0.0176904
\(708\) −3.63240 −0.136514
\(709\) −1.94456 −0.0730294 −0.0365147 0.999333i \(-0.511626\pi\)
−0.0365147 + 0.999333i \(0.511626\pi\)
\(710\) 25.2289 0.946824
\(711\) 3.26200 0.122335
\(712\) 8.78717 0.329313
\(713\) −9.08138 −0.340100
\(714\) 21.5193 0.805339
\(715\) 119.500 4.46905
\(716\) 1.60008 0.0597977
\(717\) 18.1739 0.678718
\(718\) −40.8125 −1.52311
\(719\) 13.5879 0.506742 0.253371 0.967369i \(-0.418461\pi\)
0.253371 + 0.967369i \(0.418461\pi\)
\(720\) 4.62266 0.172276
\(721\) 39.0089 1.45277
\(722\) 32.3768 1.20494
\(723\) 12.7023 0.472402
\(724\) 4.43702 0.164901
\(725\) 11.9019 0.442024
\(726\) 23.7637 0.881955
\(727\) 37.3198 1.38412 0.692058 0.721842i \(-0.256704\pi\)
0.692058 + 0.721842i \(0.256704\pi\)
\(728\) −52.1309 −1.93210
\(729\) 23.4201 0.867411
\(730\) 37.7132 1.39583
\(731\) 28.1437 1.04093
\(732\) −2.47404 −0.0914431
\(733\) −16.8847 −0.623650 −0.311825 0.950139i \(-0.600940\pi\)
−0.311825 + 0.950139i \(0.600940\pi\)
\(734\) −30.1458 −1.11270
\(735\) −4.16474 −0.153619
\(736\) 1.45860 0.0537646
\(737\) 9.02051 0.332275
\(738\) −1.13845 −0.0419069
\(739\) −22.1714 −0.815588 −0.407794 0.913074i \(-0.633702\pi\)
−0.407794 + 0.913074i \(0.633702\pi\)
\(740\) 7.05655 0.259404
\(741\) −76.6046 −2.81414
\(742\) −4.84219 −0.177762
\(743\) −1.45976 −0.0535535 −0.0267767 0.999641i \(-0.508524\pi\)
−0.0267767 + 0.999641i \(0.508524\pi\)
\(744\) 49.3956 1.81093
\(745\) −34.5479 −1.26574
\(746\) −10.0148 −0.366666
\(747\) −3.79213 −0.138747
\(748\) 3.85670 0.141015
\(749\) 11.0264 0.402897
\(750\) −68.3040 −2.49411
\(751\) −16.9248 −0.617596 −0.308798 0.951128i \(-0.599927\pi\)
−0.308798 + 0.951128i \(0.599927\pi\)
\(752\) 19.7402 0.719849
\(753\) 18.2801 0.666164
\(754\) −8.39360 −0.305677
\(755\) −3.70528 −0.134849
\(756\) −3.47660 −0.126443
\(757\) 23.6215 0.858539 0.429270 0.903176i \(-0.358771\pi\)
0.429270 + 0.903176i \(0.358771\pi\)
\(758\) −19.1652 −0.696112
\(759\) 8.33613 0.302582
\(760\) 80.8674 2.93337
\(761\) −15.3396 −0.556059 −0.278029 0.960573i \(-0.589681\pi\)
−0.278029 + 0.960573i \(0.589681\pi\)
\(762\) 5.78402 0.209533
\(763\) 4.76112 0.172364
\(764\) −1.19008 −0.0430556
\(765\) 4.40438 0.159241
\(766\) −42.9935 −1.55342
\(767\) −48.7965 −1.76194
\(768\) −11.1670 −0.402954
\(769\) −32.1320 −1.15871 −0.579355 0.815075i \(-0.696696\pi\)
−0.579355 + 0.815075i \(0.696696\pi\)
\(770\) 68.1084 2.45446
\(771\) −8.89165 −0.320225
\(772\) −3.85705 −0.138818
\(773\) −0.152416 −0.00548201 −0.00274101 0.999996i \(-0.500872\pi\)
−0.00274101 + 0.999996i \(0.500872\pi\)
\(774\) −3.76047 −0.135167
\(775\) −108.085 −3.88254
\(776\) −6.75159 −0.242368
\(777\) −33.1658 −1.18982
\(778\) −39.5549 −1.41811
\(779\) −17.2867 −0.619361
\(780\) −12.3883 −0.443571
\(781\) −21.2512 −0.760427
\(782\) −4.29064 −0.153433
\(783\) −4.87295 −0.174145
\(784\) −1.89513 −0.0676831
\(785\) −92.4313 −3.29901
\(786\) −37.6856 −1.34420
\(787\) 45.3720 1.61734 0.808669 0.588264i \(-0.200189\pi\)
0.808669 + 0.588264i \(0.200189\pi\)
\(788\) 4.36520 0.155504
\(789\) 10.2844 0.366133
\(790\) −53.7102 −1.91092
\(791\) 10.0033 0.355675
\(792\) −4.48600 −0.159403
\(793\) −33.2354 −1.18023
\(794\) 3.56997 0.126693
\(795\) −10.0171 −0.355268
\(796\) −2.76956 −0.0981645
\(797\) −43.4238 −1.53815 −0.769076 0.639158i \(-0.779283\pi\)
−0.769076 + 0.639158i \(0.779283\pi\)
\(798\) −43.6604 −1.54556
\(799\) 18.8080 0.665380
\(800\) 17.3600 0.613769
\(801\) −0.971001 −0.0343086
\(802\) 27.4885 0.970652
\(803\) −31.7672 −1.12104
\(804\) −0.935133 −0.0329796
\(805\) 11.3003 0.398283
\(806\) 76.2255 2.68493
\(807\) −36.5882 −1.28796
\(808\) 0.510128 0.0179463
\(809\) −9.14016 −0.321351 −0.160675 0.987007i \(-0.551367\pi\)
−0.160675 + 0.987007i \(0.551367\pi\)
\(810\) 53.5846 1.88277
\(811\) −26.0277 −0.913957 −0.456979 0.889478i \(-0.651068\pi\)
−0.456979 + 0.889478i \(0.651068\pi\)
\(812\) 0.713450 0.0250372
\(813\) 23.3706 0.819641
\(814\) 39.8561 1.39696
\(815\) 30.3874 1.06443
\(816\) 20.2571 0.709139
\(817\) −57.1007 −1.99770
\(818\) −11.3055 −0.395286
\(819\) 5.76058 0.201291
\(820\) −2.79556 −0.0976251
\(821\) −2.03323 −0.0709603 −0.0354802 0.999370i \(-0.511296\pi\)
−0.0354802 + 0.999370i \(0.511296\pi\)
\(822\) −48.6374 −1.69642
\(823\) −5.62311 −0.196009 −0.0980047 0.995186i \(-0.531246\pi\)
−0.0980047 + 0.995186i \(0.531246\pi\)
\(824\) 42.3053 1.47378
\(825\) 99.2155 3.45424
\(826\) −27.8113 −0.967680
\(827\) 16.9600 0.589757 0.294878 0.955535i \(-0.404721\pi\)
0.294878 + 0.955535i \(0.404721\pi\)
\(828\) −0.0854998 −0.00297132
\(829\) −29.3835 −1.02053 −0.510265 0.860017i \(-0.670453\pi\)
−0.510265 + 0.860017i \(0.670453\pi\)
\(830\) 62.4390 2.16729
\(831\) 23.9304 0.830137
\(832\) −55.6788 −1.93032
\(833\) −1.80564 −0.0625617
\(834\) 21.5367 0.745756
\(835\) 7.81009 0.270279
\(836\) −7.82483 −0.270627
\(837\) 44.2531 1.52961
\(838\) 17.1521 0.592509
\(839\) 22.6490 0.781931 0.390966 0.920405i \(-0.372141\pi\)
0.390966 + 0.920405i \(0.372141\pi\)
\(840\) −61.4648 −2.12074
\(841\) 1.00000 0.0344828
\(842\) 29.8660 1.02925
\(843\) 7.25290 0.249803
\(844\) 6.25659 0.215361
\(845\) −112.975 −3.88644
\(846\) −2.51306 −0.0864009
\(847\) −27.1347 −0.932359
\(848\) −4.55817 −0.156528
\(849\) −7.37558 −0.253129
\(850\) −51.0666 −1.75157
\(851\) 6.61278 0.226683
\(852\) 2.20306 0.0754755
\(853\) −3.58645 −0.122798 −0.0613988 0.998113i \(-0.519556\pi\)
−0.0613988 + 0.998113i \(0.519556\pi\)
\(854\) −18.9424 −0.648195
\(855\) −8.93602 −0.305605
\(856\) 11.9582 0.408723
\(857\) 35.4173 1.20983 0.604916 0.796290i \(-0.293207\pi\)
0.604916 + 0.796290i \(0.293207\pi\)
\(858\) −69.9701 −2.38874
\(859\) −45.0733 −1.53788 −0.768941 0.639320i \(-0.779216\pi\)
−0.768941 + 0.639320i \(0.779216\pi\)
\(860\) −9.23415 −0.314882
\(861\) 13.1391 0.447779
\(862\) −42.0247 −1.43137
\(863\) −31.8710 −1.08490 −0.542451 0.840087i \(-0.682504\pi\)
−0.542451 + 0.840087i \(0.682504\pi\)
\(864\) −7.10767 −0.241808
\(865\) 3.26955 0.111168
\(866\) −18.5630 −0.630797
\(867\) −11.7188 −0.397990
\(868\) −6.47911 −0.219915
\(869\) 45.2420 1.53473
\(870\) −9.89645 −0.335521
\(871\) −12.5623 −0.425657
\(872\) 5.16345 0.174856
\(873\) 0.746066 0.0252505
\(874\) 8.70526 0.294460
\(875\) 77.9931 2.63665
\(876\) 3.29322 0.111268
\(877\) 46.5013 1.57024 0.785119 0.619345i \(-0.212602\pi\)
0.785119 + 0.619345i \(0.212602\pi\)
\(878\) 11.6378 0.392758
\(879\) 16.3325 0.550882
\(880\) 64.1134 2.16126
\(881\) 46.8173 1.57731 0.788657 0.614834i \(-0.210777\pi\)
0.788657 + 0.614834i \(0.210777\pi\)
\(882\) 0.241263 0.00812376
\(883\) 19.4950 0.656059 0.328030 0.944667i \(-0.393615\pi\)
0.328030 + 0.944667i \(0.393615\pi\)
\(884\) −5.37097 −0.180645
\(885\) −57.5334 −1.93397
\(886\) −44.6927 −1.50148
\(887\) 30.4696 1.02307 0.511534 0.859263i \(-0.329077\pi\)
0.511534 + 0.859263i \(0.329077\pi\)
\(888\) −35.9684 −1.20702
\(889\) −6.60451 −0.221508
\(890\) 15.9879 0.535917
\(891\) −45.1362 −1.51212
\(892\) −0.245169 −0.00820885
\(893\) −38.1595 −1.27696
\(894\) 20.2286 0.676547
\(895\) 25.3435 0.847141
\(896\) −23.7155 −0.792278
\(897\) −11.6092 −0.387620
\(898\) 5.16444 0.172340
\(899\) −9.08138 −0.302881
\(900\) −1.01761 −0.0339202
\(901\) −4.34293 −0.144684
\(902\) −15.7896 −0.525736
\(903\) 43.4005 1.44428
\(904\) 10.8486 0.360818
\(905\) 70.2778 2.33611
\(906\) 2.16953 0.0720779
\(907\) 30.3091 1.00640 0.503199 0.864171i \(-0.332156\pi\)
0.503199 + 0.864171i \(0.332156\pi\)
\(908\) −5.27260 −0.174977
\(909\) −0.0563703 −0.00186968
\(910\) −94.8502 −3.14425
\(911\) −5.21341 −0.172728 −0.0863639 0.996264i \(-0.527525\pi\)
−0.0863639 + 0.996264i \(0.527525\pi\)
\(912\) −41.0995 −1.36094
\(913\) −52.5945 −1.74063
\(914\) −26.1997 −0.866609
\(915\) −39.1862 −1.29545
\(916\) −1.78201 −0.0588792
\(917\) 43.0314 1.42102
\(918\) 20.9081 0.690069
\(919\) 25.4577 0.839774 0.419887 0.907577i \(-0.362070\pi\)
0.419887 + 0.907577i \(0.362070\pi\)
\(920\) 12.2552 0.404042
\(921\) 5.65717 0.186410
\(922\) −21.7131 −0.715083
\(923\) 29.5952 0.974137
\(924\) 5.94741 0.195655
\(925\) 78.7045 2.58779
\(926\) 33.6373 1.10539
\(927\) −4.67483 −0.153542
\(928\) 1.45860 0.0478808
\(929\) −25.6824 −0.842614 −0.421307 0.906918i \(-0.638428\pi\)
−0.421307 + 0.906918i \(0.638428\pi\)
\(930\) 89.8735 2.94707
\(931\) 3.66345 0.120065
\(932\) 2.56423 0.0839941
\(933\) −8.05995 −0.263871
\(934\) −30.1020 −0.984967
\(935\) 61.0860 1.99773
\(936\) 6.24736 0.204201
\(937\) 31.5910 1.03203 0.516017 0.856579i \(-0.327414\pi\)
0.516017 + 0.856579i \(0.327414\pi\)
\(938\) −7.15981 −0.233776
\(939\) 21.9255 0.715511
\(940\) −6.17104 −0.201277
\(941\) −11.2334 −0.366197 −0.183099 0.983095i \(-0.558613\pi\)
−0.183099 + 0.983095i \(0.558613\pi\)
\(942\) 54.1208 1.76335
\(943\) −2.61975 −0.0853109
\(944\) −26.1800 −0.852088
\(945\) −55.0658 −1.79129
\(946\) −52.1554 −1.69572
\(947\) 3.53968 0.115024 0.0575120 0.998345i \(-0.481683\pi\)
0.0575120 + 0.998345i \(0.481683\pi\)
\(948\) −4.69012 −0.152328
\(949\) 44.2401 1.43609
\(950\) 103.609 3.36152
\(951\) 51.3601 1.66546
\(952\) −26.6483 −0.863676
\(953\) −19.3911 −0.628139 −0.314070 0.949400i \(-0.601693\pi\)
−0.314070 + 0.949400i \(0.601693\pi\)
\(954\) 0.580288 0.0187875
\(955\) −18.8496 −0.609960
\(956\) −2.58528 −0.0836138
\(957\) 8.33613 0.269469
\(958\) 57.3584 1.85317
\(959\) 55.5368 1.79338
\(960\) −65.6480 −2.11878
\(961\) 51.4715 1.66037
\(962\) −55.5051 −1.78956
\(963\) −1.32141 −0.0425817
\(964\) −1.80692 −0.0581970
\(965\) −61.0916 −1.96661
\(966\) −6.61660 −0.212886
\(967\) −25.7607 −0.828409 −0.414204 0.910184i \(-0.635940\pi\)
−0.414204 + 0.910184i \(0.635940\pi\)
\(968\) −29.4277 −0.945841
\(969\) −39.1587 −1.25796
\(970\) −12.2843 −0.394424
\(971\) −1.98623 −0.0637411 −0.0318706 0.999492i \(-0.510146\pi\)
−0.0318706 + 0.999492i \(0.510146\pi\)
\(972\) 0.884662 0.0283755
\(973\) −24.5918 −0.788377
\(974\) −1.41772 −0.0454268
\(975\) −138.171 −4.42501
\(976\) −17.8313 −0.570766
\(977\) 62.0767 1.98601 0.993004 0.118080i \(-0.0376738\pi\)
0.993004 + 0.118080i \(0.0376738\pi\)
\(978\) −17.7926 −0.568944
\(979\) −13.4672 −0.430413
\(980\) 0.592443 0.0189249
\(981\) −0.570572 −0.0182170
\(982\) 16.4030 0.523441
\(983\) 10.1811 0.324726 0.162363 0.986731i \(-0.448088\pi\)
0.162363 + 0.986731i \(0.448088\pi\)
\(984\) 14.2494 0.454254
\(985\) 69.1401 2.20299
\(986\) −4.29064 −0.136642
\(987\) 29.0039 0.923203
\(988\) 10.8971 0.346684
\(989\) −8.65344 −0.275163
\(990\) −8.16210 −0.259409
\(991\) 37.7804 1.20013 0.600067 0.799950i \(-0.295141\pi\)
0.600067 + 0.799950i \(0.295141\pi\)
\(992\) −13.2461 −0.420563
\(993\) 33.7956 1.07247
\(994\) 16.8676 0.535008
\(995\) −43.8670 −1.39068
\(996\) 5.45234 0.172764
\(997\) −58.3762 −1.84879 −0.924396 0.381435i \(-0.875430\pi\)
−0.924396 + 0.381435i \(0.875430\pi\)
\(998\) −9.83583 −0.311348
\(999\) −32.2238 −1.01951
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 667.2.a.a.1.7 10
3.2 odd 2 6003.2.a.l.1.4 10
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
667.2.a.a.1.7 10 1.1 even 1 trivial
6003.2.a.l.1.4 10 3.2 odd 2